### 110.5.5 Cohomology

Papers discussing cohomology of sheaves on algebraic stacks.

• Olsson: Sheaves on Artin stacks

This paper develops the theory of quasi-coherent and constructible sheaves proving basic cohomological properties. This paper corrects a mistake in [LM-B] in the functoriality of the lisse-étale site. The cotangent complex is constructed. In addition, the following theorems are proved: Grothendieck's Fundamental Theorem for proper morphisms, Grothendieck's Existence Theorem, Zariski's Connectedness Theorem and finiteness theorem for proper pushforwards of coherent and constructible sheaves.
• Behrend: Derived $l$-adic categories for algebraic stacks

Proves the Lefschetz trace formula for algebraic stacks.
• Behrend: Cohomology of stacks

Defines the de Rham cohomology for differentiable stacks and singular cohomology for topological stacks.
• Faltings: Finiteness of coherent cohomology for proper fppf stacks

Proves coherence for direct images of coherent sheaves for proper morphisms.
• Abramovich, Corti, Vistoli: Twisted bundles and admissible covers [acv]

The appendix contains the proper base change theorem for étale cohomology for tame Deligne-Mumford stacks.

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